# Connecting Graph

Medium

## Question

Given n nodes in a graph labeled from 1 to n . There is no edges in the graph at beginning.

You need to support the following method:
1) connect(a, b), add an edge to connect node a and node b .
2) query(a, b), check if two nodes are connected

Example

``````5 // n = 5
query(1, 2) return false
connect(1, 2)
query(1, 3) return false
connect(2, 4)
query(1, 4) return true
``````

## Thinking

Add an edge to connect node a and node b DOES NOT mean the edge from node a to node b. The edge maybe between some nodes which are A parent and B parent.

## Review

Since n is known, we can use an array to store roots.

## Solution

In this solution, we use root of each nodes to connect two nodes.

#### Java (Review)

``````public class ConnectingGraph {

private int[] roots = null;

public ConnectingGraph(int n) {
// initialize your data structure here.
roots = new int[n + 1]; // we don't use index 0
for (int i = 1; i <= n; i++) {
roots[i] = i;
}
}

public void connect(int a, int b) {
int rootA = getRoot(a);
int rootB = getRoot(b);
if (rootA != rootB) {
roots[rootA] = rootB; // connect a and b by root
}
}

public boolean  query(int a, int b) {
return getRoot(a) == getRoot(b);
}

private int getRoot(int node) {
if (roots[node] == node) {
return node;
}
int root = getRoot(roots[node]);
roots[node] = root;
return root;
}
}
``````

#### Java

``````public class ConnectingGraph {

private Map<Integer, Integer> rootMap = new HashMap<Integer, Integer>();

public ConnectingGraph(int n) {
// initialize your data structure here.
for (int i = 1; i <= n; i++) {
rootMap.put(i, i);
}
}

public void connect(int a, int b) {
int rootA = getRoot(a);
int rootB = getRoot(b);
if (rootA != rootB) {
rootMap.put(rootA, rootB);
}
}

public boolean  query(int a, int b) {
return getRoot(a) == getRoot(b);
}

private int getRoot(int node) {
Integer root = rootMap.get(node);
if (root == null) {
rootMap.put(node, node);
return node;
}
if (root == node) {
return node;
}
root = getRoot(root);
rootMap.put(node, root);
return root;
}

}
``````